On 3-Transitive Transformation Groups of the Lobachevskii Plane
- Authors: Nigmatullina L.I.1, Sosov E.N.1
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Affiliations:
- Lobachevskii Institute of Mathematics and Mechanics
- Issue: Vol 39, No 9 (2018)
- Pages: 1403-1406
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203452
- DOI: https://doi.org/10.1134/S1995080218090433
- ID: 203452
Cite item
Abstract
In this paper, we consider three transformation groups of the Lobachevskii plane that are generated by the group of all motions and one-parameter transformation groups, which preserve an elliptic, a hyperbolic or a parabolic bundle of straight lines of this plane, respectively. It is proved that each of these groups acts 3-transitively on the Lobachevskii plane. The transformation groups and their generalizations can be applied an research of quasi-conformal mappings of the Lobachevskii space, in the special theory of relativity and in the fractal geometry.
About the authors
L. I. Nigmatullina
Lobachevskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: leysan.nigmatullina@bk.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008
E. N. Sosov
Lobachevskii Institute of Mathematics and Mechanics
Email: leysan.nigmatullina@bk.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008